I'd like to add, that playing a Daimyo isn't fun due to strange mechanisms in the Shogunate system. The limitation of diplomatic actions caused by the Shogunate Influence cause more problem than the basically good idea is worth. Not all limitations seem to make sense and even as Shogun a high Influence can often times be disadvantageous. Since there is no proper way to reduce influence, this leads to explotive measures, like multiple selections of "Endorse Culture" to force your own Prestige down in order to lose Influence. Also pointless missions aiming for the Emperor keep firing for the Daimyos. Please do something about these issues in the next patch! After all DW is kind of about Asia and the brilliant balancing (kudos, seriously!!!) of the four Daimyos would make 1399 Japan an ideal MP scenario - but not in the condition it is in momentarily.
I'd just like to point out that it is pretty easy to decrease the shogunate influence, just get into bad relations with the other Daymo's and don't get your prestige up so high. It helps that Japan gets all the infamy+prestige from outside wars. There are still some diplomacy bugs in the system though. That and there are a quite a few missions that are almost impossible, because you need to have a NI for it.